Problem: A unicorn daycare center requires there to be $2$ supervisors for every $18$ baby unicorns. Write an equation that shows the relationship between $n$, the number of supervisors, and $u$, the number of baby unicorns. Please note that this is a magical daycare center, so fractional supervisors are allowed.
Solution: Let's find the constant of proportionality. In the proportional relationship between $n$, the number of supervisors, and $u$, the number of baby unicorns, one constant of proportionality is the ratio of baby unicorns to supervisors. It is the number we multiply by the number of supervisors to get the number of baby unicorns. $n\,\times\, ?=u$ $\begin{aligned} n\,\times\, {?}&=u \\\\ {?}&=\dfrac{u}{n} \\\\ &=\dfrac{18}{2} \\\\ &={9} \end{aligned}$ The constant of proportionality is ${9}$. This means we can multiply ${9}$ by the number of supervisors to get the number of baby unicorns. Now, let's write the equation: $\begin{aligned} \text{baby unicorns}&={\text{baby unicorn to supervisor ratio}}\times\text{supervisors} \\\\ u&={9}n \end{aligned}$ One correct equation is: $u = 9n$